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We had this question at a game a few months ago, and settled it exactly like that. There's nothing really hinting one way or another in the rules book (at least in the French translation!), but it seems reasonable to me.
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F'xOct 23 '10 at 20:16

A. No, neither cards from your hand nor cards in play in front of you. ... [T]he character Sid Ketchum can discard exactly 2 cards when he chooses so to regain one life point.

Also, the creator explained that other cards with the icon are not the same as a Beer card. They can be used to restore life points when only two players are in play, and can also be played without effect when your life points are full. However, they can't be used to restore your last life point (or played outside of phase 2 of your turn for any other reason).

I think yes, because it's like using a Panic on a player with no cards. Here is why:

Beer has an effective range of [Casting Player]. It automatically hits the person who plays it without fail. Since it is not out of range, it can be played.

Panic has an effective range of [1]. If you are going to compare the two, you must assume that the player being targeted is also in range, just as the Beer casting player is in range of the card "Beer".

This is a more fair comparison than Tycho's because both cards can technically be played at this point, but neither will be able to have its intended effect; Beer wont be able to restore the health point since the player is at max and Panic wont be able to draw a card from a player because that player doesn't have a card to draw.

The new question is "Can you play cards that have no effect?" The answer to this is most likely yes. One in game clue to this is that the character "Apache Kid." He is unaffected by diamonds, yet this does not mean you cannot play a diamond on him. The diamond card will simply have no effect. If we carry this rule on to normal play, one should be able to Beer them self when at full health.

I actually don't believe you can play a beer if you cannot take the effect just as you could not play a panic if both players next to you had an appaloosa. By my reading of the rules the only way to willingly discard a card is to have more cards than your hand limit at the end of your turn.

Also, Kevin is correct that you may only play a beer out of turn on a lethal hit.